Angular Frequency Switching of Holonomy-Based Motion Planning for the Second-Order Chained Form System

This paper addresses a motion planning problem of the second-order chained form system. One of the authors previously proposed a holonomy-based motion planning method using sinusoidal functions as control inputs. In the conventional method, the basis is to extract holonomy whose magnitude depends to amplitude-related parameters of control inputs. It is, however, unclear whether or not such a holonomy-based motion planning can be adjustable with respect to time. This paper reveals the relation between holonomy and the angular frequency of control inputs, which extends the conventional method. The effectiveness of the extended method is numerically demonstrated through an application to an underactuated manipulator.